Electronic Structure of Copper Impurities in ZnO

Abstract

We have measured the near infrared absorption, Zeeman effect, and electron spin resonance of ${\mathrm{Cu}}^{2+}$ ions introduced as a substitutional impurity into single-crystal ZnO. From the $g$ values of the lowest ${\ensuremath{\Gamma}}_{6}$ component of the ${T}_{2}$ state (the ground state), ${g}_{\mathrm{II}}=0.74$ and ${g}_{\ensuremath{\perp}}=1.531$, and from the $g$ values of the ${\ensuremath{\Gamma}}_{4}{\ensuremath{\Gamma}}_{5}$ component of the $E$ state, ${g}_{\mathrm{II}}=1.63$ and ${g}_{\ensuremath{\perp}}=0$, we have determined the wave functions of ${\mathrm{Cu}}^{2+}$ in terms of an LCAO MO model in which overlap only with the first nearest neighbor oxygen ions is considered. These wave functions indicate that the copper $3d$ (${t}_{2}$) hole spends about 40% of its time in the oxygen orbitals, and that the copper ${t}_{2}$ orbitals are expanded radially with respect to the $e$ orbitals. Corroboration for the radial expansion of the ${t}_{2}$ orbitals is obtained from an analysis of the hyperfine splitting. It is concluded from our model that the large values of the hyperfine constants, $|A|=195\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $|B|=231\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, are due to the contribution from the orbital motion of the ${t}_{2}$ hole.